Design models may be subject to a variety of perturbations or uncertainties, such as in variables, parameters and the constraint right-hand sides. In this paper, we study the specific cases of deterministic variations in the variables and the parameters. The goal is to obtain designs that not only reduce cost but which are also insensitive to such perturbations. We formulate bilevel models for this purpose and illustrate with examples the nature of insensitive designs, as well as the singularities that occur in such bilevel models.

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